Vectors
Bayani Gaba-gaba
A delivery drone needs more than a distance to reach its target: it needs a direction too. Fly 4 km the wrong way and you are further from the parcel than when you started. Vectors are the tool mathematics uses to carry size and direction together, and they turn awkward geometry problems, where a diagram only gets you so far, into clean algebra.
This topic builds vector notation and column vectors from the ground up, covers addition, subtraction, scalar multiplication and magnitude, and finishes with the technique examiners favour most: using vectors to prove that lines are parallel, that points are collinear, and that several lines meet at a single point.
Manufura
- Understand scalar and vector quantities in two dimensions
- Understand and use vector notation including column vectors
- Represent a vector by a directed line segment
- Understand and use parallel vectors, unit vectors and position vectors
- Find the sum and difference of two vectors
- Calculate the modulus (magnitude) of a vector
- Multiply a vector by a scalar
- Find the resultant of two or more vectors
- Apply vector methods to simple geometrical problems including collinearity, parallel lines and concurrency
Taswirar tunani
An zana wannan batu don ka ga yadda ra'ayoyi ke hadewa.
Bude taswirar tunani a cikin manhaja
Katunan tunawa
Gwaji mai sauri kan abin da ake jarraba a wannan batu.
Yi atisayen wadannan katuna a cikin manhaja
Takardar Darasi
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Sami manhajar Green Bridge CBT a wayarka ko kwamfutarka domin cikakken laburaren IGCSE: takardun jarrabawar baya, tsarin kimantawa, taswirar tunani, katunan karatu da darussan sauti.
Nazarin Darasi
Barka da kammala darasi akan Vectors. Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- Which of these is a vector quantity? A) Mass B) Temperature C) Velocity D) Area Answer: C
- What is the magnitude of the vector (8, -6)? A) 2 B) 10 C) 14 D) 100 Answer: B
- If a = (5, -2) and b = (-3, 6), what is a - b? A) (2, 4) B) (8, -8) C) (-8, 8) D) (2, -4) Answer: B
- Multiplying a vector by -3 will: A) triple its magnitude and keep the same direction B) triple its magnitude and reverse its direction C) divide its magnitude by 3 and reverse its direction D) keep the magnitude the same and reverse its direction Answer: B
- P, Q and R have position vectors such that PQ = 2(PR). What can you conclude? A) P, Q and R are collinear B) PQ is perpendicular to PR C) Q is the midpoint of PR D) Nothing can be concluded Answer: A
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
Vectors
View vectors geometrically.
"Algebra and Trigonometry: Vectors" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/10-8-vectors. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Wasu ƙungiyoyi ne suka wallafa su ƙarƙashin lasisin buɗe, kuma muna ambaton su yadda suka nema. Hanyoyin suna buɗe shafukansu.
Yi Aikin Tambayoyin Gwaji
Kana son yin aikin tambayoyin gwaji kan Vectors? Sauke manhajar Green Bridge CBT don samun tambayoyin gwaji da cikakkun jarrabawa akan wannan batu.
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Duk abin da kake buƙata don yin fice a JAMB, WAEC & NECO.
